The carnist claims that an animal is already dead at the time of purchase, so purchasing an animal product is not unethical.
By purchasing the product you're creating demand for the product. If a grocery store sells fewer steaks, they order fewer from the supplier, who orders fewer cows to be slaughtered, which in turn creates fewer cows.
Yes, that feedback process is not instantaneous. No one is waiting with a knife in the back of the grocery store to kill an animal. That still doesn't mean that creating a demand for that product and normalizing its use to those around you is ethical.
Would you question buying a product from a store if I confirmed for you that it was created using slave labor? What if I told you "You can have this wallet - oh I got it from a guy I killed." Would you think any differently about it? What's it matter? He's already dead.